Model based and experimental investigation of respiratory effect on the HRV power spectrum.

The role of respiration in the genesis of heart rate variability (HRV) has been the subject matter of many experimental and modeling studies. It is widely accepted that the high frequency (HF) peak of a HRV power spectrum, which is centered at the average respiratory frequency, is caused by mechanisms activated by respiration. On the other hand, there is a debate on the possible role of respiration in the genesis of the low frequency (LF) peak which is usually centered around 0.1 Hz. In this study, a comprehensive cardiorespiratory interaction model is used to test various hypotheses regarding the role of respiration in the LF peak of HRV. In this model, chest and abdomen circumference signals and lung volume signal are used as respiratory inputs. Simulations are made for periodic, spontaneous and slightly irregular respiratory patterns, and it is observed that the more low frequency (LF) power there in the respiratory signals, the more LF power there in the model-predicted HRV. Experiments on nine volunteers are also performed for the same respiratory patterns and similar results are observed. Furthermore, the actual measured respiratory signals are input to the model and the model predicted and the actual HRVs are compared both in time domain and also with respect to their power spectra. It is concluded in general that respiration not only is the major contributor to the genesis of the HF peak in the HRV power spectrum, but also plays an important role in the genesis of its LF peak. Thus, the LF/HF ratio, which is used to assess sympathovagal balance, cannot be correctly utilized in the absence of simultaneous monitoring of respiration during an HRV test.

Model based analysis of the variation in Korotkoff sound onset time during exercise.

In this study, a minimal mathematical model of the cardiovascular system is used to study the effects of changes in arterial compliance and cardiac contractility on the onset time of Korotkoff sounds during an auscultatory procedure. The model provides blood pressure waveforms in the ventricle, the aorta and the brachial artery. From these waveforms, pre-ejection time, pulse propagation time and rise time of the blood pressure at the brachial artery can be computed. The time delay between onset time of ECG Q wave and onset time of Korotkoff sound is the sum of these three times. Rise time is zero and the time delay is minimal when the cuff pressure is slightly above the diastolic pressure. This minimum time delay is represented by QKD. Simulation results suggest that during the Bruce exercise protocol QKD decreases to one-third of its pre-exercise value if the cardiac contractility increases threefold. The effect of arterial compliance is not as significant as that of the cardiac contractility. From data recorded during an exercise test, it is observed that QKD decreases considerably as the test load is increased. We show in this study that the amount of decrease in QKD can be used as an index of the amount of increase in cardiac contractility during an exercise ECG test. Use of signal averaging for reducing the effect of motion artifacts during an exercise test is also shown to be very instrumental for making accurate QKD measurements.

Measurement of AC magnetic field distribution using magnetic resonance imaging.

Electric currents are applied to body in numerous applications in medicine such as electrical impedance tomography, cardiac defibrillation, electrocautery, and physiotherapy. If the magnetic field within a region is measured, the currents generating these fields can be calculated using the curl operator. In this study, magnetic fields generated within a phantom by currents passing through an external wire is measured using a magnetic resonance imaging (MRI) system. A pulse sequence that is originally designed for mapping static magnetic field inhomogeneity is adapted. AC current in the form of a burst sine wave is applied synchronously with the pulse sequence. The frequency of the applied current is in the audio range with an amplitude of 175-mA rms. It is shown that each voxel value of sequential images obtained by the proposed pulse sequence is modulated similar to a single tone broadband frequency modulated (FM) waveform with the ac magnetic field strength determining the modulation index. An algorithm is developed to calculate the ac magnetic field intensity at each voxel using the frequency spectrum of the voxel signal. Experimental results show that the proposed algorithm can be used to calculate ac magnetic field distribution within a conducting sample that is placed in an MRI system.

A method for comparative evaluation of EIT algorithms using a standard data set.

The point spread function (PSF) is the most widely used tool for quantifying the spatial resolution of imaging systems. However, prerequisites for the proper use of this tool are linearity and space invariance. Because EIT is non-linear it is only possible to compare different reconstruction algorithms using a standard data set. In this study, the FEM is used to generate simulation data, which are used to investigate the non-linear behaviour of EIT, the space dependence of its PSF and its capability of resolving nearby objects. It is found that for the case of iterative backprojection (IterB), the full width half maximum (FWHM) values of single-object perturbations for central, intermediate and peripheral high-contrast objects are 27%, 18% and 14% of the imaging region diameter respectively. For the method based on singular value decomposition of the Geselowitz lead sensitivity matrix (GS-SVD), the FWHM is not space dependent and is 12% of the imaging region diameter. Conclusions obtained using single-object PSF studies must also be checked with double-object or more complex perturbations because EIT is non-linear. For example, the GS-SVD method fails to detect two widely separated objects unless the truncation level of SVD is carefully adjusted. With more truncation, however, the resolution of the method is worsened. Based on these and similar observations a set of simulation data, which is proposed for comparative evaluation of different EIT algorithms, is specified and explained in the conclusion section.

Removal of power line interference in signal-averaged electrocardiography systems.

A method for line interference reduction to be used in signal-averaged electrocardiography (SAECG) systems is proposed and its performance is analyzed. This new method is an adaptation of a previously reported technique for removal of line interference from conventional electrocardiograms. It involves the recording of a line reference signal simultaneous with the lead signals, so that a shifted and scaled version of it can be used to subtract line interference from the leads. It is shown that this line interference subtraction method can reduce line interference effectively and without introducing any additional noise into the ECG signal. It is also shown that Late Potential diagnostic decisions are not altered when this filter is applied. It is recommended that this technique be used in SAECG when line interference is unavoidable.

Distribution of aortic mechanical prosthetic valve closure sound model parameters on the surface of the chest.

It has been previously proposed that heart valve closure sounds can be modeled by a sum of decaying sinusoids, based on the hypothesis that the heart cavity, heart walls, major vessels, and other structures in the chest constitute a frequency selective linear acoustic system and this system is excited by the rapidly decelerating valve occluder. In this study, distribution of the parameters of this model for the second heart sound is investigated. For this purpose, heart sounds of 10 patients who have a St. Jude-type bileaflet mechanical heart valve prosthesis in aortic position are recorded. Recordings are performed at 12 different locations on the surface of the chest. To reliably assign representative parameters to each recording site, signal averaging, model order selection, and a special filtration technique are employed. The results of the analyses are discussed in relation to the above hypothesis on the heart sound generation mechanism. It is observed that site-to-site variation of frequencies of modes does not exceed the accuracy limit of proposed analysis method, but energies of these modes vary on the surface of the chest, and as a result of statistical analysis, it appears that energy of some modes are significantly different between two recording sites.

A fast image reconstruction algorithm for electrical impedance tomography.

In this paper, we propose a fast algorithm for the reconstruction of the conductivity perturbation delta sigma about a known conductivity variation sigma omicron. The method is based on the minimization of a quadratic functional subject to linear constraints, where the existence of a unique solution is guaranteed. The algorithm developed for this purpose is iterative and each iteration is composed of a simple matrix multiplication. The validity of this method is illustrated with several examples.

A comparative study of several exciting magnetic fields for induced current EIT.

In this study, the selection of coil configuration parameters (coil radius and coil centre shift) for induced current EIT using circular coils is investigated. An alternative coil configuration is suggested, which produces approximately linear (spatially) magnetic fields in order to strengthen the currents in the central region. Injected current EIT, with Sheffield data collection protocol, and induced current EIT, with two different coil configurations, are compared with respect to singular-value patterns, sensitivity distributions and imaging performances. It is observed that for the proposed alternative coil configuration the measurements are more sensitive to inner region conductivity perturbations when compared to injected current EIT and induced current EIT using circular coils. The images obtained by induced current EIT are comparable to that obtained by injected current EIT.

Electrical impedance tomography using induced currents.

The mathematical basis of a new imaging modality, induced current electrical impedance tomography (EIT), is investigated, The ultimate aim of this technique is the reconstruction of conductivity distribution of the human body, from voltage measurements made between electrodes placed on the surface, when currents are induced inside the body by applied time varying magnetic fields. In this study the two-dimensional problem is analyzed. A specific 9-coil system for generating nine different exciting magnetic fields (50 kHz) and 16 measurement electrodes around the object are assumed, The partial differential equation for the scaler potential function in the conductive medium is derived and finite element method (FEM) is used for its solution. Sensitivity matrix, which relates the perturbation in measurements to the conductivity perturbations, is calculated. Singular value decomposition of the sensitivity matrix shows that there are 135 independent measurements. It is found that measurements are less sensitive to changes in conductivity of the object's interior. While in this respect induced current EIT is slightly inferior to the technique of injected current EIT (using Sheffield protocol), its sensitivity matrix is better conditioned. The images obtained are found to be comparable to injected current EIT images In resolution. Design of a coil system for which parameters such as sensitivity to inner regions and condition number of the sensitivity matrix are optimum, remains to be made.

Analysis of three-dimensional software EIT (electrical impedance tomography) phantoms by the finite element method.

In electrical impedance tomography, two-dimensional (2D) finite element solutions are used in the imaging algorithms. It is assumed that a major part of the current flowing through the object is restricted to the measurement plane (i.e. the plane determined by the electrodes which are used for measuring voltage differences) and the current flowing elsewhere is negligible. However, there is usually a three-dimensional (3D) variation of the conductivity distribution and if there are regions of high contrast close to the measurement plane, the measured voltage values may be considerably affected. In this work a 3D finite element analysis is utilised to demonstrate the previously mentioned effects. Examples are given to show the measured voltage differences for conductivity distributions which are identical on the measurement plane but different elsewhere.

Electrical impedance tomography. Determination of the boundary of an object inserted into a water-filled cylinder.

In order to circumvent the electrode position determination problem in static electrical impedance tomography, it is possible to insert the object to be imaged into a water-filled cylinder on which the electrodes are at fixed and known positions. It has previously been shown that if the boundary of the internally placed object and the conductivity of the salty water in the cylinder are known, then a significant improvement in the conductivity image of the object is obtained. An algorithm for finding the boundary of an internally placed object is developed based on the finite element method (FEM). The boundary is assumed to obey a parametric model and the parameters are estimated by inverting a matrix representing the sensitivity of the boundary voltage measurements to parameter variations. The algorithm assumes that the object's internal conductivity is uniform and known. Simulation studies show that if the internal conductivity is not uniform to the extent found in the arm cross-sections, up to 9% error in the boundary, as measured from a centrally placed reference point, may result. It is also shown that if previous knowledge about the boundary shape is used to model the boundary with fewer numbers of parameters, then the boundary may be found with less error.

Electrical impedance tomography using induced and injected currents.

A two-dimensional forward problem formulation is introduced for electrical impedance tomography (EIT) using induced currents. The forward problem is linearised around a certain resistivity distribution and the inverse problem is formulated as a solution of a linear system of equations. Sensitivity of boundary measurements to resistivity variations are analysed for spatially uniform, linear and quadratic fields. The formulation, however, is suitable for studying the effects of a general magnetic field applied to induce the currents in the conductive object. A similar inverse problem formulation is also developed for EIT using injected currents. Simulation studies are performed by reconstructing images of a simulation distribution using both methods separately with generalised inversion. It is also shown that the derived formulations for the inverse problems of the two methods can be combined to solve a larger set of equations with a greater number of independent measurements.

A new technique for line interference monitoring and reduction in biopotential amplifiers.

It has been reported that power line frequency must be accurately known if line interference is to be accurately subtracted from the output of a bipotential amplifier. In this paper, hardware developed to record the common mode line frequency signal on the body simultaneously with the ECG lead signals of a 15-channel computerized cardiograph is described. This interference reference signal and its quadrature, obtained by software, are linearly combined to be subtracted from any one of the channels to reduce line interference to below the quantization level of the 12 b A/D converter. Coefficients of the linear combination are estimated using linear regression which is applied to the relatively isoelectric regions of the data, excluding the QRS complexes. Since the interference reference signal is available in real time, simultaneously with the ECG signals, another software approach is also adopted in which an adaptive interference reduction algorithm is used to cope with varying interference. A recursive least squares algorithm with forgetting factor is used to update the coefficients. This updating mechanism is gated by the output of a software QRS detector. Results regarding the performance of both the off-line and the adaptive algorithms are given, and the effects of nonisoelectric portions of the ECG lead signals on the estimation of the coefficients are quantified.

Electrical impedance tomography of translationally uniform cylindrical objects with general cross-sectional boundaries.

An algorithm is developed for electrical impedance tomography (EIT) of finite cylinders with general cross-sectional boundaries and translationally uniform conductivity distributions. The electrodes for data collection are assumed to be placed around a cross-sectional plane; therefore, the axial variation of the boundary conditions and the potential field are expanded in Fourier series. For each Fourier component a two-dimensional (2-D) partial differential equation is derived. Thus the 3-D forward problem is solved as a succession of 2-D problems, and it is shown that the Fourier series can be truncated to provide substantial savings in computation time. The finite element method is adopted and the accuracy of the boundary potential differences (gradients) thus calculated is assessed by comparison to results obtained using cylindrical harmonic expansions for circular cylinders. A 1016-element and 541-node mesh is found to be optimal. The algorithm is applied to data collected from phantoms, and the errors incurred from the several assumptions of the method are investigated.

Quantitative estimation of insulin sensitivity.

We have evaluated the feasibility of using a mathematical model of glucose disappearance to estimate insulin sensitivity. Glucose was injected into conscious dogs at 100, 200, or 300 mg/kg. The measured time course of insulin was regarded as the "input," and the falling glucose concentration as the "output" of the physiological system storing and using glucose. Seven mathematical models of glucose uptake were compared to identify the representation most capable of simulating glucose disappearance. One specific nonlinear model was superior in that it 1) predicted the time course of glucose after glucose injection, 2) had four parameters that could be precisely estimated, and 3) described individual experiments with similar parameter values. Insulin sensitivity index (SI), defined as the dependence of fractional glucose disappearance on plasma insulin, was the ratio of two parameters of the chosen model and could be estimated with good reproducibility from the 300 mg/kg injection experiments (SI = 7.00 X 10(-4) +/- 24% (coefficient of variation) min-1/(microU/ml) (n = 8)). Thus, from a single glucose injection it is possible to obtain a quantitative index of insulin sensitivity that may have clinical applicability.